VertexShapeFunction is an option and property for Graph and related functions that specifies a function to use to generate primitives for rendering each vertex.
EdgeShapeFunction is an option and property for Graph and related functions that specifies a function to use to generate primitives for rendering each edge.
These "How tos" give step-by-step instructions for common tasks related to editing and manipulating graphics in Mathematica .
VertexList[g] gives a list of all vertices in the graph g.
New Graphic creates a new graphic at the insertion point.
VertexShape is an option and property for Graph and related functions that specifies the graphics used for vertices.
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GraphPower[g, n] gives the graph-n\[Null]^th power of the graph g.